Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen���Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

Conflicting claims problem associated with cost sharing of a network

A minimum cost spanning tree (mcst) problem analyzes the way to efficiently connect individuals to a source when they are located at different places. Once the efficient tree is obtained, the question on how allocating the total cost among the involved agents defines, in a natural way, a confliicting claims situation. For instance, we may consider the endowment as the total cost of the network, whereas for each individual her claim is the maximum amount she will be allocated, that is, her connection cost to the source. Obviously, we have a confliicting claims problem, so we can apply claims rules in order to obtain an allocation of the total cost. Nevertheless, the allocation obtained by using claims rules might not satisfy some appealing properties (in particular, it does not belong to the core of the associated cooperative game). We will define other natural claims problems that appear if we analyze the maximum and minimum amount that an individual should pay in order to support the minimum cost tree. Keywords: Minimum cost spanning tree problem, Claims problem, Core JEL classification: C71, D63, D71.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j���{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with ��(G) ��� 4, BBC(G,T) = ��(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ��� uv ��� T, |f(u)-f(v)|=2 or |f(u)-f(v)| ��� k-2, k = ��(G). For the case that G is a planar graph, according to Four Colour Theorem, ��(G) = 4; so, BBC(G,T) = 4.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Results of n-alkane biomarker analyses and paleoclimate reconstruction

The current study presents quantitative reconstructions of tree cover, annual precipitation and mean July temperature derived from the pollen record from Lake Billyakh (65��17'N, 126��47'E, 340 m above sea level) spanning the last ca. 50 kyr. The reconstruction of tree cover suggests presence of woody plants through the entire analyzed time interval, although trees played only a minor role in the vegetation around Lake Billyakh prior to 14 kyr BP (<5%). This result corroborates low percentages of tree pollen and low scores of the cold deciduous forest biome in the PG1755 record from Lake Billyakh. The reconstructed values of the mean temperature of the warmest month ~8-10 ��C do not support larch forest or woodland around Lake Billyakh during the coldest phase of the last glacial between ~32 and ~15 kyr BP. However, modern cases from northern Siberia, ca. 750 km north of Lake Billyakh, demonstrate that individual larch plants can grow within shrub and grass tundra landscape in very low mean July temperatures of about 8 ��C. This makes plausible our hypothesis that the western and southern foreland of the Verkhoyansk Mountains could provide enough moist and warm microhabitats and allow individual larch specimens to survive climatic extremes of the last glacial. Reconstructed mean values of precipitation are about 270 mm/yr during the last glacial interval. This value is almost 100 mm higher than modern averages reported for the extreme-continental north-eastern Siberia east of Lake Billyakh, where larch-dominated cold deciduous forest grows at present. This suggests that last glacial environments around Lake Billyakh were never too dry for larch to grow and that the summer warmth was the main factor, which limited tree growth during the last glacial interval. The n-alkane analysis of the Siberian plants presented in this study demonstrates rather complex alkane distribution patterns, which challenge the interpretation of the fossil records. In particular, extremely low n-alkane concentrations in the leaves of local coniferous trees and shrubs suggest that their contribution to the litter and therefore to the fossil lake sediments might be not high enough for tracing the Quaternary history of the needleleaved taxa using the n-alkane biomarker method.

Node sampling using random centrifugal walks

Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the source, with a given probability distribution. All these algorithms are based on a new class of random walks, that we call Random Centrifugal Walks (RCW). A RCW is a random walk that starts at the source and always moves away from it. Firstly, an algorithm to sample any connected network using RCW is proposed. The algorithm assumes that each node has a weight, so that the sampling process must select a node with a probability proportional to its weight. This algorithm requires a preprocessing phase before the sampling of nodes. In particular, a minimum diameter spanning tree (MDST) is created in the network, and then nodes weights are efficiently aggregated using the tree. The good news are that the preprocessing is done only once, regardless of the number of sources and the number of samples taken from the network. After that, every sample is done with a RCW whose length is bounded by the network diameter. Secondly, RCW algorithms that do not require preprocessing are proposed for grids and networks with regular concentric connectivity, for the case when the probability of selecting a node is a function of its distance to the source. The key features of the RCW algorithms (unlike previous Markovian approaches) are that (1) they do not need to warm-up (stabilize), (2) the sampling always finishes in a number of hops bounded by the network diameter, and (3) it selects a node with the exact probability distribution.

Extended formulations, nonnegative factorizations, and randomized communication protocols

An extended formulation of a polyhedron P is a linear description of a polyhedron Q together with a linear map �� such that ��(Q)=P. These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject of a number of studies. Yannakakis��� factorization theorem (Yannakakis in J Comput Syst Sci 43(3):441���466, 1991) provides a surprising connection between extended formulations and communication complexity, showing that the smallest size of an extended formulation of $$P$$P equals the nonnegative rank of its slack matrix S. Moreover, Yannakakis also shows that the nonnegative rank of S is at most 2^c, where c is the complexity of any deterministic protocol computing S. In this paper, we show that the latter result can be strengthened when we allow protocols to be randomized. In particular, we prove that the base-2 logarithm of the nonnegative rank of any nonnegative matrix equals the minimum complexity of a randomized communication protocol computing the matrix in expectation. Using Yannakakis��� factorization theorem, this implies that the base-2 logarithm of the smallest size of an extended formulation of a polytope P equals the minimum complexity of a randomized communication protocol computing the slack matrix of P in expectation. We show that allowing randomization in the protocol can be crucial for obtaining small extended formulations. Specifically, we prove that for the spanning tree and perfect matching polytopes, small variance in the protocol forces large size in the extended formulation.

Reconfiguration of distribution networks to minimize loss and disruption costs using genetic algorithms

In this paper a computational implementation of an evolutionary algorithm (EA) is shown in order to tackle the problem of reconfiguring radial distribution systems. The developed module considers power quality indices such as long duration interruptions and customer process disruptions due to voltage sags, by using the Monte Carlo simulation method. Power quality costs are modeled into the mathematical problem formulation, which are added to the cost of network losses. As for the EA codification proposed, a decimal representation is used. The EA operators, namely selection, recombination and mutation, which are considered for the reconfiguration algorithm, are herein analyzed. A number of selection procedures are analyzed, namely tournament, elitism and a mixed technique using both elitism and tournament. The recombination operator was developed by considering a chromosome structure representation that maps the network branches and system radiality, and another structure that takes into account the network topology and feasibility of network operation to exchange genetic material. The topologies regarding the initial population are randomly produced so as radial configurations are produced through the Prim and Kruskal algorithms that rapidly build minimum spanning trees. (C) 2009 Elsevier B.V. All rights reserved.

A layer 2 multipath fabric using a centralized controller

Disserta����o para obten����o do Grau de Mestre em Engenharia Electrot��cnica e de Computadores

The concept of exchangeability in ensemble forecasting

A set of random variables is exchangeable if its joint distribution function is invariant under permutation of the arguments. The concept of exchangeability is discussed, with a view towards potential application in evaluating ensemble forecasts. It is argued that the paradigm of ensembles being an independent draw from an underlying distribution function is probably too narrow; allowing ensemble members to be merely exchangeable might be a more versatile model. The question is discussed whether established methods of ensemble evaluation need alteration under this model, with reliability being given particular attention. It turns out that the standard methodology of rank histograms can still be applied. As a first application of the exchangeability concept, it is shown that the method of minimum spanning trees to evaluate the reliability of high dimensional ensembles is mathematically sound.

Algoritomos transgen��ticos aplicados ao problema da ��rvore geradora biobjetivo

The Multiobjective Spanning Tree is a NP-hard Combinatorial Optimization problem whose application arises in several areas, especially networks design. In this work, we propose a solution to the biobjective version of the problem through a Transgenetic Algorithm named ATIS-NP. The Computational Transgenetic is a metaheuristic technique from Evolutionary Computation whose inspiration relies in the conception of cooperation (and not competition) as the factor of main influence to evolution. The algorithm outlined is the evolution of a work that has already yielded two other transgenetic algorithms. In this sense, the algorithms previously developed are also presented. This research also comprises an experimental analysis with the aim of obtaining information related to the performance of ATIS-NP when compared to other approaches. Thus, ATIS-NP is compared to the algorithms previously implemented and to other transgenetic already presented for the problem under consideration. The computational experiments also address the comparison to two recent approaches from literature that present good results, a GRASP and a genetic algorithms. The efficiency of the method described is evaluated with basis in metrics of solution quality and computational time spent. Considering the problem is within the context of Multiobjective Optimization, quality indicators are adopted to infer the criteria of solution quality. Statistical tests evaluate the significance of results obtained from computational experiments

Uma an��lise experimental de algoritmos exatos aplicados ao problema da ��rvore geradora multiobjetivo

The Multiobjective Spanning Tree Problem is NP-hard and models applications in several areas. This research presents an experimental analysis of different strategies used in the literature to develop exact algorithms to solve the problem. Initially, the algorithms are classified according to the approaches used to solve the problem. Features of two or more approaches can be found in some of those algorithms. The approaches investigated here are: the two-stage method, branch-and-bound, k-best and the preference-based approach. The main contribution of this research lies in the fact that no research was presented to date reporting a systematic experimental analysis of exact algorithms for the Multiobjective Spanning Tree Problem. Therefore, this work can be a basis for other research that deal with the same problem. The computational experiments compare the performance of algorithms regarding processing time, efficiency based on the number of objectives and number of solutions found in a controlled time interval. The analysis of the algorithms was performed for known instances of the problem, as well as instances obtained from a generator commonly used in the literature

Speeding up optimum-path forest training by path-cost propagation

In this paper we present an optimization of the Optimum-Path Forest classifier training procedure, which is based on a theoretical relationship between minimum spanning forest and optimum-path forest for a specific path-cost function. Experiments on public datasets have shown that the proposed approach can obtain similar accuracy to the traditional one but with faster data training. �� 2012 ICPR Org Committee.

Evaluation of ERIC-PCR as Genotyping Method for Corynebacterium pseudotuberculosis Isolates

Conselho Nacional de Desenvolvimento Cient��fico e Tecnol��gico (CNPq)

Intera����es entre pr��-escolares: possibilidades de an��lises

Buscou-se, neste trabalho, construir a rede de rela����es sociais entre pr��-escolares e analisar a pertin��ncia das metodologias utilizadas para a coleta e an��lise dos dados. Participaram dezessete pr��-escolares de uma escola privada em Bel��m-PA. Os dados foram coletados atrav��s de teste sociom��trico e observa����o comportamental. A estrutura do grupo foi analisada a partir da rede de rela����es sociais, constru��da atrav��s de ��rvores Geradoras M��nimas (Teoria dos Grafos). Os resultados mostraram prefer��ncias por parcerias diferentes no teste sociom��trico e no comportamento interativo. As duas medidas complementaram-se. O uso da Teoria dos Grafos demonstrou-se relevante por possibilitar an��lises quantitativa e qualitativa do fen��meno social.